WCIPEG 2017-2018 Test

The Carol Economy is a set of people who interact and share hearts (<3) with each other. In order to be part of the Carol Economy, each person must be friends with every other person. Carol is trying to set up a larger Carol economy between some of her friends. There are ~N~ people, and ~K~ pairs of people know each other. Help Carol calculate the amount of new friendships that must be made.

Input Specification

The first line of input contains the integers ~N~ ~(1 \le N \le 1\,000)~ and ~K~ ~(0 \le K \le 10^6)~.

Output Specification

Output the number of new friendships that must be made. This number is guaranteed to be non-negative.

Sample Input

10 8

Sample Output

37